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In the past, the Webster optimal cycle time formula was limited to calculate the optimal cycle from historical data for fixed-time traffic signal control. This paper focuses on the design of an adaptive traffic signal control based on fuzzy logic with Webster and modified Webster's formula. These formulas are used to calculate the optimal cycle time depending on the current traffic situation which applying in the next cycle. The alternation of the traffic condition between two successive cycles is monitored and handled through the fuzzy logic system to compensate the fluctuation. The obtained optimal cycle time is used to determine adaptively the effective phase green times i.e. is used to determine adaptively the maximum allowable extension limit of the green phase in the next cycle. The SUMO traffic simulator is used to compare the results of the proposed adaptive control methods with fuzzy logic based traffic control, and a fixed-time Webster and modified Webster based traffic control methods. The proposed methods are tested on an isolated intersection. In this study, real field-collected data obtained from three, four, and five approaches intersections in Kilis/Turkey are used to test the performance of the proposed methods. In addition, to examine the efficiency of the proposed techniques at heavy demands, the arbitrary demands are generated by SUMO for a four approaches intersection. The obtained simulation results indicate that the proposed methods over perform the fixed time and fuzzy logic based traffic control methods in terms of average vehicular delay, speed, and travel time.INDEX TERMS Fuzzy logic control, Webster's formula, modified Webster's formula, adaptive traffic control, fixed-time traffic control, SUMO simulator.

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